Abstract
We propose a private information retrieval (PIR) protocol for distributed storage systems with noncolluding nodes
where data is stored using an arbitrary linear code. An expression for the PIR rate, i.e., the ratio of the amount of
retrieved data per unit of downloaded data, is derived, and a necessary and a sufficient condition for codes to
achieve the maximum distance separable (MDS) PIR capacity are given. The necessary condition is based on the
generalized Hamming weights of the storage code, while the sufficient condition is based on code
automorphisms. We show that cyclic codes and Reed-Muller codes satisfy the sufficient condition and are thus
MDS-PIR capacity-achieving.